Four-pile caps made from concrete are essential elements for the force transfer from the superstructure to piles or pipes. Due to the difficulties in carrying out full-scale tests and all the instrumentation involved, the use of numerical models as a way to study the mechanical behavior of these elements presents itself as a good alternative. Such numerical studies usually provide useful information for the update and improvement of normative standards and codes. The concrete damaged plasticity (CDP) constitutive model, which combines damage and plasticity with smeared-crack propagation, stands out in the simulation of reinforced concrete. This model is composed of five parameters: dilatation angle (ψ), eccentricity (ϵ), ratio between biaxial and uniaxial compressive strength (σ_bo/σ_co), failure surface in the deviator plane normal to the hydrostatic axis (K_c), and viscosity (μ). For unidimensional elements, the values of the CDP parameters are well defined, but for volumetric elements, such as concrete pile caps, there is a gap in the literature regarding the definition of these values. This fact ends up limiting the use of the CDP on these structural elements due to the uncertainties involved. Therefore, the aim of this research was to calibrate two numerical models of concrete four-pile caps with different failure modes for the evaluation of the sensitivity of the CDP parameters, except for ϵ, which remained constant. As a result, the parameters σ_bo/σ_co and K_c did not significantly influence the calibration of the force × displacement curves of the simulated structures. Values of ψ and μ equal to 36° and 1 × 10⁻⁴, respectively, are recommended for “static” analysis, while for “quasi-static” analysis, ψ values ranging between 45° and 50° are suggested according to the failure mode. The results also showed to be sensitive to the constitutive relation of concrete tensile behavior in both modes of analysis. For geometric parameterization, the “static” analysis is recommended due to the lower coefficient of variation (3.29%) compared to the “quasi-static” analysis (19.18%). This conclusion is supported by the evaluation of the ultimate load of the numerical models from the geometrically parametric study compared to the results estimated by an analytical model.

This paper discusses the use of confinement in over-reinforced concrete beams. This reinforcement consists of square stirrups, placed in the compression zone of the beam cross-section, in order to improve its ductility. A parametric numerical study is initially performed, using a finite element computational program that considers the material nonlinearities and the confinement effect. To investigate the influence of the transverse reinforcing ratio on the beam ductility, an experimental program was also conducted. Four over-reinforced beams were tested; three beam specimens with additional transverse reinforcement to confine the beams, and one without it. All specimens were fabricated with a concrete designed for a compressive strength of 25 MPa. The experimental results show that the post-peak ductility factor is proportional to the confining reinforcement ratio, however the same is not observed for the pre-peak ductility factor, which varied randomly with changes in the confining reinforcement ratio. It was also observed from the experiments that the confinement effect tends to be smaller close to the beam neutral axis.

Pile caps can be dimensioned using, preferably, plastic models (strut-and-tie) and models based on the flexion theory. In order to analyze the behavior of the stresses in the lower and upper nodal regions of the cap, a theoretical analysis of the experimental results found by several researchers was made. There was a discrepancy in the results obtained and, as a result, a critical analysis carried out and a new methodology for the verification of the nodal stress near the upper zone, based on the multiaxial behavior of the concrete, is suggested.

Pile caps are structural elements used to transfer loads from the superstructure to a group of piles. The design of caps is normally based on analytical formulations, considering the strut and tie method. Through the advance of computational technology, the use of an integrated soil and foundation model may suggest a behavioral trend to obtain a more realistic modeling for the structural element being studied. This work aimed at analyzing, in numerical fashion, the structural behavior of reinforced concrete two-pile caps considering the lateral friction between the piles and the ground through a continuous modeling, as well as to analyze the portion of the load that is transferred to the ground directly by the cap. The lateral friction was modeled considering node coupling and through contact elements. Simulations were performed considering three soil types (sandy, clayish, and soilless), three cap heights, and three pile lengths. Soil parameters were obtained through semi-empirical correlations. Through these analyses, the conclusion was reached that, on average, 4.50% of the force applied to the pillar is transferred directly to the ground by cap. In terms of the principal compression stresses, in the superior nodal region, the strut tends to form beyond the section of the column. Alternatively, increasing cap stiffness provided, on average, an increase in the load carrying capacity of the models.

Technical literature provides experimental campaign results for four-pile caps with significant value in structural engineering. However, failure modes and measurement of these specimens are particularly challenging due to their volumetric nature. These experimental records are frequently utilized to evaluate analytical models focusing on less conservative than normative models to predict rupture force. Moreover, recent studies emphasize the necessity of developing simplified predictive models. In this context, the objective of this study was to evaluate the feasibility of regression models for estimating the rupture force associated with strut failure. The evaluation was based on a commonly used database and employed analysis of variance (ANOVA) at a 5% significance level to identify critical variables. The regression models were developed with variable interactions incorporated into the equations in three forms: (i) without interaction, (ii) with linear interaction, and (iii) with quadratic interaction. An analysis of the developed regression models identified a model with satisfactory accuracy. This model achieved an average predicted force ratio of 1.00 (COV = 14%) for the database and 1.03 (COV = 16.68%) for extrapolated numeric models in finite elements with the concrete damaged and plasticity (CDP) constitutive model, initially calibrated with experimental tests. A methodology was proposed to assist in the initial design of four-pile caps.